UPSC Prelims 2022 · CSAT
Question 59: Basic Numeracy
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm :
- 1.It is possible to cut the sheet exactly into 4 square sheets.
- 2.It is possible to cut the sheet into 10 triangular sheets of equal area.
Which of the above statements is/are correct?
AnswerUPSC’s answer is (c).
Statement 1: cut off an 8 × 8 square, then another 8 × 8, leaving 4 × 8, which splits into two 4 × 4 squares. That is 4 squares (sides 8, 8, 4, 4) with no waste, so it is possible. Statement 2: cut five 4 × 8 strips along the length, then cut each along its diagonal. That gives 10 right triangles of area 16 each, all equal. Both are possible.
- 1. Squares of sides 8, 8, 4 and 4 tile the 20 × 8 sheet exactly.
- 2. Five 4 × 8 strips, each cut along a diagonal, give 10 equal triangles.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: Squares of sides 8, 8, 4 and 4 tile the 20 × 8 sheet exactly.
- Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: Five 4 × 8 strips, each cut along a diagonal, give 10 equal triangles.
Only (c) is left. This one needs every statement.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: statement 2 also holds.
- (b) Wrong: statement 1 also holds.
- (c) Correct: both cuts can be made.
- (d) Wrong: both statements hold.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.